Homework Help:
The law of conservation of energy problem!

hello, I been doing physics homework and I came across this problem that i think i know how to do but for some reason i cannot get the right answer! any help will be very appreciated
thanks a lot:)

1. The problem statement, all variables and given/known data

The highest waterfall in Canada is the Della Falls in B.C. with a change in elevation of 440 m m. When the water has fallen 12% of its way to the bottom, its speed is 33 m/s. Neglecting air resistance and fluid friction, determine the speed of the water at the top of the waterfall.

answer in the book: 5.0 m/s

2. Relevant equations

Ek = 1/2 mv^2

Ep = mgh

3. The attempt at a solution

This is what i tried,

i found what 12% of 440 m is, and it ended up to equal 52.8 so i subtracted it by 440 m to get 387.2 m as the height after the water has fallen 12% of its way to the bottom.

Ek1 + Ep1 = Ek2 + Ep2

(masses cancel out) and we are left with

1/2 v^2 + gh = 1/2 v^2 + gh

1/2 v^2 + (9.81)(440) = 1/2 (33)^2 + (9.81)(387.2)

and i get v= 66 m/s (dont think it is right but it is possible that the book might be wrong)

Draw a sketch of the waterfall, and everything the question told you about the waterfall. Then mark on the value you got for the speed of the water at the top of the waterfall, and the value that the book got.

Once you've done this, you'll be able to figure out which answer is definitely wrong. Then you'll know whether you need some help with your calculation or not.